LAPACK 3.12.0
LAPACK: Linear Algebra PACKage

◆ dlasd3()

subroutine dlasd3 ( integer  NL,
integer  NR,
integer  SQRE,
integer  K,
double precision, dimension( * )  D,
double precision, dimension( ldq, * )  Q,
integer  LDQ,
double precision, dimension( * )  DSIGMA,
double precision, dimension( ldu, * )  U,
integer  LDU,
double precision, dimension( ldu2, * )  U2,
integer  LDU2,
double precision, dimension( ldvt, * )  VT,
integer  LDVT,
double precision, dimension( ldvt2, * )  VT2,
integer  LDVT2,
integer, dimension( * )  IDXC,
integer, dimension( * )  CTOT,
double precision, dimension( * )  Z,
integer  INFO 
)

DLASD3 finds all square roots of the roots of the secular equation, as defined by the values in D and Z, and then updates the singular vectors by matrix multiplication. Used by sbdsdc.

Download DLASD3 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DLASD3 finds all the square roots of the roots of the secular
 equation, as defined by the values in D and Z.  It makes the
 appropriate calls to DLASD4 and then updates the singular
 vectors by matrix multiplication.

 DLASD3 is called from DLASD1.
Parameters
[in]NL
          NL is INTEGER
         The row dimension of the upper block.  NL >= 1.
[in]NR
          NR is INTEGER
         The row dimension of the lower block.  NR >= 1.
[in]SQRE
          SQRE is INTEGER
         = 0: the lower block is an NR-by-NR square matrix.
         = 1: the lower block is an NR-by-(NR+1) rectangular matrix.

         The bidiagonal matrix has N = NL + NR + 1 rows and
         M = N + SQRE >= N columns.
[in]K
          K is INTEGER
         The size of the secular equation, 1 =< K = < N.
[out]D
          D is DOUBLE PRECISION array, dimension(K)
         On exit the square roots of the roots of the secular equation,
         in ascending order.
[out]Q
          Q is DOUBLE PRECISION array, dimension (LDQ,K)
[in]LDQ
          LDQ is INTEGER
         The leading dimension of the array Q.  LDQ >= K.
[in]DSIGMA
          DSIGMA is DOUBLE PRECISION array, dimension(K)
         The first K elements of this array contain the old roots
         of the deflated updating problem.  These are the poles
         of the secular equation.
[out]U
          U is DOUBLE PRECISION array, dimension (LDU, N)
         The last N - K columns of this matrix contain the deflated
         left singular vectors.
[in]LDU
          LDU is INTEGER
         The leading dimension of the array U.  LDU >= N.
[in]U2
          U2 is DOUBLE PRECISION array, dimension (LDU2, N)
         The first K columns of this matrix contain the non-deflated
         left singular vectors for the split problem.
[in]LDU2
          LDU2 is INTEGER
         The leading dimension of the array U2.  LDU2 >= N.
[out]VT
          VT is DOUBLE PRECISION array, dimension (LDVT, M)
         The last M - K columns of VT**T contain the deflated
         right singular vectors.
[in]LDVT
          LDVT is INTEGER
         The leading dimension of the array VT.  LDVT >= N.
[in,out]VT2
          VT2 is DOUBLE PRECISION array, dimension (LDVT2, N)
         The first K columns of VT2**T contain the non-deflated
         right singular vectors for the split problem.
[in]LDVT2
          LDVT2 is INTEGER
         The leading dimension of the array VT2.  LDVT2 >= N.
[in]IDXC
          IDXC is INTEGER array, dimension ( N )
         The permutation used to arrange the columns of U (and rows of
         VT) into three groups:  the first group contains non-zero
         entries only at and above (or before) NL +1; the second
         contains non-zero entries only at and below (or after) NL+2;
         and the third is dense. The first column of U and the row of
         VT are treated separately, however.

         The rows of the singular vectors found by DLASD4
         must be likewise permuted before the matrix multiplies can
         take place.
[in]CTOT
          CTOT is INTEGER array, dimension ( 4 )
         A count of the total number of the various types of columns
         in U (or rows in VT), as described in IDXC. The fourth column
         type is any column which has been deflated.
[in,out]Z
          Z is DOUBLE PRECISION array, dimension (K)
         The first K elements of this array contain the components
         of the deflation-adjusted updating row vector.
[out]INFO
          INFO is INTEGER
         = 0:  successful exit.
         < 0:  if INFO = -i, the i-th argument had an illegal value.
         > 0:  if INFO = 1, a singular value did not converge
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA